Wouter Marco Kouw

Bayesian inference offers a principled account of information processing in natural agents. However, it remains an open question how neural mechanisms perform their abstract operations. We investigate a hypothesis where a distributed form of Bayesian inference, namely message passing on factor graphs, is performed by a simulated network of leaky-integrate-and-fire neurons. Specifically, we perform Gaussian belief propagation by encoding messages that come into factor nodes as spike-based signals, propagating these signals through a spiking neural network and decoding the spike-based signal back to an outgoing message. Three core linear operations, equality (branching), addition, and multiplication, are realized in networks of leaky integrate-and-fire models. Validation against the standard sum-product algorithm shows accurate message updates, while applications to Kalman filtering and Bayesian linear regression demonstrate the framework's potential for both static and dynamic inference tasks. Our results provide a step toward biologically grounded, neuromorphic implementations of probabilistic reasoning.

This letter extends the exactly sparse Gaussian variational inference (ESGVI) algorithm for state estimation in two complementary directions. First, ESGVI is generalized to operate on matrix Lie groups, enabling the estimation of states with orientation components while respecting the underlying group structure. Second, factors are introduced to accommodate heavy-tailed and skewed noise distributions, as commonly encountered in ultra-wideband (UWB) localization due to non-line-of-sight (NLOS) and multipath effects. Both extensions are shown to integrate naturally within the ESGVI framework while preserving its sparse and derivative-free structure. The proposed approach is validated in a UWB localization experiment with NLOS-rich measurements, demonstrating improved accuracy and comparable consistency. Finally, a Python implementation within a factor-graph-based estimation framework is made open-source to support broader research use.

Bayesian inference offers a principled account of information processing in natural agents. However, it remains an open question how neural mechanisms perform their abstract operations. We investigate a hypothesis where a distributed form of Bayesian inference, namely message passing on factor graphs, is performed by a simulated network of leaky-integrate-and-fire neurons. Specifically, we perform Gaussian belief propagation by encoding messages that come into factor nodes as spike-based signals, propagating these signals through a spiking neural network (SNN) and decoding the spike-based signal back to an outgoing message. Three core linear operations, equality (branching), addition, and multiplication, are realized in networks of leaky integrate-and-fire models. Validation against the standard sum-product algorithm shows accurate message updates, while applications to Kalman filtering and Bayesian linear regression demonstrate the framework's potential for both static and dynamic inference tasks. Our results provide a step toward biologically grounded, neuromorphic implementations of probabilistic reasoning.

We present a Forney-style factor graph representation for the class of multivariate autoregressive models with exogenous inputs, and we propose an online Bayesian parameter-identification procedure based on message passing within this graph. We derive message-update rules for (1) a custom factor node that represents the multivariate autoregressive likelihood function and (2) the matrix normal Wishart distribution over the parameters. The flow of messages reveals how parameter uncertainty propagates into predictive uncertainty over the system outputs and how individual factor nodes and edges contribute to the overall model evidence. We evaluate the message-passing-based procedure on (i) a simulated autoregressive system, demonstrating convergence, and (ii) on a benchmark task, demonstrating strong predictive performance.

Accurate prediction of ship trajectories is crucial for ensuring safe and efficient navigation. However, predicting ship trajectories in complex and dynamic environments presents significant challenges. Ships exhibit multi-mode motions, manifesting as diverse motion patterns even under similar circumstances, influenced by factors such as navigational intentions and operational tasks. Moreover, trajectory prediction is further complicated by time-varying ship dynamics, encompassing sailing conditions, ship maneuvering, and environmental factors. In this paper, we propose a Bayesian multiple model with an online model selection strategy to dynamically represent the latent motion mode from early observations. Each sub-model integrates a variational Kalman filter and Gated Recurrent Unit (GRU) neural network, enabling the estimation of time-varying transition coefficients and the process noise specific to different motion modalities. This hybrid methodology leverages the strengths of probabilistic recursive estimation of the Kalman filter while benefiting from the capacity of a GRU network to learn complex temporal dependencies from historical data. The proposed method was evaluated on ship trajectories across different observation lengths and prediction horizons and outperformed the baseline in terms of both accuracy and plausibility.

We propose an active inference agent to identify and control a mechanical system with multiple bodies connected by joints. This agent is constructed from multiple scalar autoregressive model-based agents, coupled together by virtue of sharing memories. Each subagent infers parameters through Bayesian filtering and controls by minimizing expected free energy over a finite time horizon. We demonstrate that a coupled agent of this kind is able to learn the dynamics of a double mass-spring-damper system, and drive it to a desired position through a balance of explorative and exploitative actions. It outperforms the uncoupled subagents in terms of surprise and goal alignment.

Ship collision accidents frequently cause casualties and significant property losses. These collisions mainly occur by incorrectly interpreting the intents of other ships’ navigators. However, inferring the avoidance intents of other ships is challenging, because the uncertain motions and the long-lasting dynamic interactions during encounters usually obscure the true intents. To address this, we propose a probabilistic graph model to infer the hidden avoidance intent of ships. Specifically, the dynamic encounter evolution is expressed in a model represented by a factor graph, where the intent beliefs are accumulated and propagated over time through message passing in the graph. In the inference procedure, we develop a hybrid Bayesian inference approach, integrating a data-driven component derived from empirical priors fitted to historical data, and a model-driven component capturing the ship’s control process. We derive 9 types of intents from naturalistic ship encounters and evaluate the model on a validation split. The quantitative metrics demonstrate that, on average, the proposed procedure can accurately infer the intents 14.04 seconds in advance and outperforms the baseline in macro-averaged recall rate (0.2919) and F1-score (0.2843). Note to Practitioners —This work aims to enhance safety in ship navigation by introducing an intelligent navigation support system to prevent collisions. A significant cause of ship collision accidents is the misinterpretation of other navigators’ intents. Estimating the intents of marine traffic participants can significantly reduce collision rates. However, real-time intent inference in ship encounters poses challenges due to complex dynamics and uncertain motions. We propose a novel probabilistic graphical model that allows us to infer avoidance intents, evaluated on a naturalistic Automatic Identification System (AIS) dataset, demonstrating effectiveness in real-world scenarios. The practical implications of our work are substantial for the maritime industry. Ship captains and intelligent automated vessels can use our system to enhance situational awareness, enabling informed collision avoidance decisions. Our work aims to improve the safety and efficiency of ship navigation, reducing collision risks and ensuring the well-being of crew members and valuable cargo.